## Paradigms in Physics: Quantum Fundamentals

Course name:
Course number:
PH 425
Course credits:
3
Class meeting times:
7 hours of lecture per week
Prerequisites:
Recommended PH 213 and concurrent enrollment in MTH 341
Course description:
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.

### Schedule from NEW:

##### Homework

Day 1 M 2/13

Welcome to QF!
• Hello Video
• Ph425 Student Info
• Photo Permission

Magnetic Moment
• face Intro to Magnetic Moment

Stern-Gerlach Experiment: Measuring Electron Spin

McIntyre 1.1.0

• Spin Fermi Estimate
• Stern Gerlach Explain

Day 2 Tu 2/14

Explore the Stern-Gerlach Experiment
• group Intro to Stern-Gerlach Experiments 1
• computer Binomial Statistics Mathematica
• Statistical Analysis of the Spins Sim

Quantum State are Vectors
• face The Quantum State Postulate

Two Sequential SG Experiments
McIntyre 1.2

Three Sequential SG Experiments
• group Stern-Gerlach & Quantum Eraser
• face Mixture vs. Superposition
McIntyre 1.2.3

Day 3 W 2/15 Math Bits

Review: Complex Numbers: Rectangular Form
• Complex Numbers: Rectangular Form

Complex Conjugation
Norm
• Real Part of a Complex Number

Algebra with Complex Numbers

Review: Circle Trig
• Circle Trig Practice
• Circle Trigonometry

Complex Numbers: Exponential Form
• Circle Trig Complex
• Complex Conjugate
• Complex Numbers All Forms Practice
• Complex Rect Polar Quiz
• Complex Rectangular Practice
• Complex Rectangular Practice
• Euler's Formula
• Phase
• Representations of Complex Numbers LO1

Day 4 Th 2/16 Math Bits

Components of Vectors
• group Describing a Vector with 2 Different Coordinate Systems

Inner Products
• group Representations of Dot Products
• Orthogonal
• Orthogonal Brief

Bra-ket (Dirac) Notation
• Dirac Practice

Day 5 F 2/17

Inner Product of a Complex Vector

Review the Anatomy of SG Experiments

The Probability Postulate
• face Probability Postulate
McIntyre 1.2
• Histogram
• Measurement Probabilities
• Phase 2 LO1 LO2

• assignment_ind Probabilities of $S_z$ Measurements for Spin-1/2 in Bra-Ket Notation

Day 6 M 2/20

Practice Probability Postulate & Normalization

Determining Spin from Experiments
• Chained Stern-Gerlach

Multiple Representations of Quantum States

Relative & Overall Phase

Day 7 Tu 2/21

Determining Spin from Experiments
• group Finding Unknown States Leaving the Oven in a Spin-$\frac{1}{2}$ System
• Unknowns One Half
• Unknowns Spin-1/2 Brief

Multiple Representations of Quantum States
• group Multiple Representations of a Quantum State

Day 8 W 2/22 Mathbits

Review: Operations with Matrices
• Matrix Refresher
• Pauli
• Pauli Practice

More Operations with Matrices

Linear Transformations
• group Linear Transformations
• Commutator
• Spin Matrix

Day 9 Th 2/23 MathBits

Diagonalization
• Diagonalization
• Diagonalization Part II

Day 10 F 2/24 Math Bits

Finding Eigenvectors & Eigenvalues
• group Finding Eigenvectors and Eigenvalues
• Eigen Spin Challenge
• Eigenvectors of Pauli Matrices
• Eigenvectors of the Rotation Matrix

Eigenbases

Day 11 M 2/27

Properties of Hermitian Matrices

Day 12 Tu 2/28

Intro to Higher Spin Systems
• face Spin-1
• General State
• Spin One Intro

Projection Operators
McIntyre 2.2-2.4

Changing Bases with a Completeness Relation
• Completeness Relation Change of Basis

Day 13 W 3/1

The Projection Postulate

General Quantum Systems

Quantum Interferometer
• group Spin-1 Interferometer
• Spin One Interferometer Brief

Day 14 Th 3/2

Quantum Interferometer Cont.

Quantum Operators
• group Constructing the Spin Operators

Finding Matrix Elements
• group Finding Matrix Elements
• Matrix Elements and Completeness Relations

The Squared Spin Operator
• Spin Three Halves Operators

Day 15 F 3/3

Commutation
• Commute

Day 16 M 3/6

Quantum Expectation Values

Quantum Uncertainty

Day 17 Tu 3/7

Solving the Schrodinger Equation & Time Evolution
• face Solving the Schrodinger Equation

More Time Evolution
• Probabilities of Energy

Day 18 W 3/8

Spin Precession in a Uniform Magnetic Field
• Frequency
• Magnet

Day 19 Th 3/9

Introduction to Wavefunctions
• Wavefunction Calculations
• Wavefunctions

Day 20 F 3/10

• group Going from Spin to Wavefunction (Modified)

Day 21 M 3/13

The Infinite Square Well
• group Going from Spin to Wavefunction (Modified)
McIntyre 5.3-5.4
• ISW Expectation
• ISW Right Quarter

Day 22 Tu 3/14

Wavefunctions
McIntyre 5.1-5.2

Day 23 W 3/15

Time Evolution of a particle in an Infinite Square Well
• group Time Evolution of the ISW
• ISW Energy Measurement

Day 24 Th 3/16

Quantum Spookiness

Day 25 F 3/17

Representations of the Infinite Square Well

• face Final Exam Review Guide

Review

3/17 Th noon-2pm
Final Exam